(1 pt) Let s(e) be the distance of a truck to an intersection At timet- 0, the t

Question

(1 pt) Let s(e) be the distance of a truck to an intersection At timet- 0, the truck is 70 meters from the intersection, is Maclaurin polymomial of s(t) and use it to estimate the truck's distance intersection. At time t , the truck is 70 meters from the intersection, is ration of a =-5 m/s2. Determine the second from the intersection ater as. traveling at a velocity of 26 m/8, and begins to slow down with an acceleration of a-5mDetermine the second (Use decimal notation. Give your answer to two decimal places.) After 4 seconds the truck is mi past the intersection. help (fractions)

Explanation / Answer

The general distance expression is:
s(t) = initial distance + initial velocity multiplied by time + 1/2 (acceleration multiplied by time squared)

Putting values we get -

s(t) = 70 + (26m/s) t - 1/2 (-5 m/s/s) t^2

The first derivative is:
s'(t) = 26 + 5 t

The second derivative is:
s''(t) = 5

The Maclaurin polynomial is:
s(0) = (26 / 1!) t - (-5 / 2!) t^2

At 4 seconds, this gives:
s(4) = (26 * 4) + (5/2) 4^2
s(4) = 104 + 40
s(4) = 144 meters

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